Skip to content

Course home

3.5 Trigonometry (A-level only)

3.5 Trigonometry (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152
Question 118
a.

Show that

cos⁡2xsin⁡x+sin⁡2xcos⁡x≡csc⁡x,x≠nπ2,  n∈Z \frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \equiv \csc x, \quad x \neq \frac{n\pi}{2}, \; n \in \mathbb{Z} sinxcos2x​+cosxsin2x​≡cscx,x=2nπ​,n∈Z
[3]
b.

In a study of fluid dynamics, the pressure coefficient PPP is modeled by the equation

(cos⁡2θsin⁡θ+sin⁡2θcos⁡θ)2=7−cot⁡θ \left( \frac{\cos 2\theta}{\sin \theta} + \frac{\sin 2\theta}{\cos \theta} \right)^2 = 7 - \cot \theta (sinθcos2θ​+cosθsin2θ​)2=7−cotθ

Hence solve this equation for 0<θ<π0 < \theta < \pi0<θ<π, giving your answers to 3 significant figures as appropriate.

[5]
c.

Using the result from part (a), or otherwise, find the exact value of

∫π6π4(cos⁡2xsin⁡x+sin⁡2xcos⁡x)cot⁡x dx \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \left( \frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \right) \cot x \, dx ∫6π​4π​​(sinxcos2x​+cosxsin2x​)cotxdx
[3]
Markscheme

3.5 Trigonometry (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Trigonometry (A-level only)

225 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank